Some of the greatest physicists of the twentieth century, including Albert Einstein, consider the speed of light a sort of universal "speed limit". But over the past couple decades physicists theorized that it should be possible to break this law and get away with it -- to travel faster than the speed of light.

I. CERN Results Potentially Described

One of several possible routes to faster-than-light travel was potentially demonstrated when researchers at CERN, the European physics organization known for maintaining the Large Hadron Collider, sent high-energy particles through the Earth's crust from Geneva, Switzerland to INFN Gran Sasso Laboratory in Italy. In a result that is today highly controversial, the team claimed that the particles were observed travelling in excess of the speed of light.

Now physics theory may finally be catching up. Math researchers at the University of Adelaide -- located in the middle South of Australia -- have developed new formulas to describe the relationship between energy, mass, and velocity (which incorporates length and time) for objects traveling faster than the speed of light. The formulas modify Einstein's Theory of Special Relativity, a fundamental pillar of our understanding of the universe.

Einstein formulated his Theory of Special Relativity in 1905. [Image Source: AP]

Math professor Jim Hill, a co-author of the paper writes, "Questions have since been raised over the experimental results [from CERN] but we were already well on our way to successfully formulating a theory of special relativity, applicable to relative velocities in excess of the speed of light."

He elaborates, "Our approach is a natural and logical extension of the Einstein Theory of Special Relativity, and produces anticipated formulae without the need for imaginary numbers or complicated physics."

The study's other co-author, Dr. Barry Cox, adds, "We are mathematicians, not physicists, so we've approached this problem from a theoretical mathematical perspective... Our paper doesn't try and explain how this could be achieved, just how equations of motion might operate in such regimes."

II. Placating the Critics

The authors obviously recognize the controversy surrounding both experimental and theoretical work regarding challenging the light speed limitation attached to the special theory of relativity. Write the authors in the abstract, "In this highly controversial topic, our particular purpose is not to enter into the merits of existing theories, but rather to present a succinct and carefully reasoned account of a new aspect of Einstein's theory of special relativity, which properly allows for faster than light motion."

The paper proposes two sets of equations -- one based on an invariant set of "frame transitions", the other based on a "frame transition" with the invariance limitation removed. The authors suspect that if faster than light travel is possible, that the physical behavior of the faster-than-light travelling object is described by one of these equations.

quote: One easy way to test the idea that the speed of light might be affected by the velocity of an object is to "ping" a spacecraft in orbit around a planet such as Mars, with the transmit signals sent alternatively from each side of the earth, so that in one case the speed of earth's spin adds to the signal

This is actually very similar to how the first calculation of the speed of light was first calculated, back in 1676, using one of Jupiter's moons. Roemer used eclipses of the moon (a regular event in time terms) and measured that as the Earth and Jupiter got further away, noting the range of time delays. Apply that range to the understood orbit diameter of the Earth, he was able to first of all prove that light speed wasn't infinite, and also calculate a rough approximation. I believe he estimated around 200,000km/s when the real value is closer to 300. Still, impressive given the time.

Anyway - what you're describing has numerous equivalent tests which have been scientifically proven and show that the speed of light is constant regardless of relative velocity. What you would see, is not the Lorentz contraction, but the relative form of the Doppler effect (red shift / blue shift). It does not take the same form as the classical physics Doppler effect which applies to Sound waves (since light doesn't require a medium) - but at low speeds the results are similar.

quote: I do believe you can see the same effect using the speed of sound. No matter how fast you go, you won't make sound travel any faster

quote: Light and sound have many similar properties. They are both waves. Neither wave can be accelerated by physically moving the emitter. Both can be used to convey the passage of time. Both experience frequency acceleration and deceleration depending on the relative speed/direction of the emitter and the receiver

That certain waves, particles, anythings travel at a particular velocity is not the the relevant fact here. The key difference between light and sound is that light doesn't require a medium, thus the mechanism for the frequency acceleration and deceleration (Doppler effect) is different. Also, light, unlike sound, will always appear to be at the same speed regardless of the observers relative velocity, whereas, for example, if you're travelling at 340m/s you can measure the speed of sound at 0 m/s. Sound and light also have different implications to time. You can overtake sound because of the above fact that sound does not have to appear the same for all observers. This has no impact on time. Perhaps that means that sound is a perfect measure of time, perhaps it means that it's a poor indicator because you can be moving forward in time and measure the speed at 0m/s. However, as you approach the speed of light, in order that the speed of light should remain constant to all observers, time itself slows down. When you reach the speed of light, time effectively stops. This is why Einstein postulated that you have no opportunity to go faster than light.

This has been experimentally demonstrated with atomic clocks and orbiting the earth. Essentially, any one observer who has relative motion with respect to a second observer will observe that the other persons clock is running slower than theirs. A good way to demonstrate this is Einstein's thought experiment of a very simple clock consisting of mirrors and a light beam. The light beam reflects back and forth and each time it hits a mirror the clock 'ticks'. if you observe an object having a velocity relative to yours, the path travelled by the light will no longer be straight up and down, but a diagonal path like this: /\/\/\/\ . Due to Pythagoras we know that the hypotenuse of a triangle is a greater distance, which when combined with the constant speed of light means that you would observe that their clock has slower down. So how is it possible for both observers to observe the other persons clock as slower, and how does nature decide whos clock is actually going slower? The answer is that whichever observer changes their velocity in order to match the velocity of the other observer will be the one whos clock is behind.

They performed this experiment and noted that the clock which had been mounted on a rocket and flown around the earth had indeed experienced less time.

What this means is that to travel faster than light is to travel back in time, or that because time stops when you're travelling at the speed of light, there is never any time to accelerate any further.

Many thought experiments have been created to explain this, such as Steven Hawkings example of travelling on a train going very near the speed of light, and then throwing a ball. Does the ball have a speed faster than the speed of light? The answer is no, because the closer you get to the speed of light, the slower time becomes in the train so the ball is adding less and less velocity to the train.

"That certain waves, particles, anythings travel at a particular velocity is not the the relevant fact here. The key difference between light and sound is that light doesn't require a medium, thus the mechanism for the frequency acceleration and deceleration (Doppler effect) is different. "

We don't really know this (light not requiring a medium) for certain. We only know that we have not found anything. However, I'm not going to argue either way since I'm not really suggesting that there is some kind of cosmic soup that we can't really observe with current technology. I'm just saying that I'm not ruling it out. I really doubt that we've quite discovered all there is to know about fabric of space. We do know that sound requires molecules to propagate.

In any event, my observation here is that one cannot affect the speed of a sound wave. However, if you listen to the Doppler Effect, by listening to an ambulance for instance, you'll notice that there are more oscillations as it approaches over a period of, say, ten seconds, than when it leaves. Thus, time is compressed, albeit, to the ear. I am saying that light does the same thing to the eye.

The experiment done with the rocket could easily be explained by the effect that gravity has on photons. There's also the possibility that stress can cause issues with the accuracy of a clock. There is also the fact that, relatively speaking, it doesn't matter which object is expending energy to achieve a difference in velocity. Relatively speaking, if you sit on either the rocket or in the chair, it's not going to make a difference.

" When you reach the speed of light, time effectively stops. This is why Einstein postulated that you have no opportunity to go faster than light."

I would simply say that if you reach the speed of light, it would appear that time has effectively stopped. But, that's only because you're travelling with the time frame.

With the train+ball visualization, if we had a different medium in which to observe both train and ball, than light, we would see the ball exceed the speed of light. However, because light is our best medium for observing high speeds, it cannot accurately describe such high velocities.

Not just the perception, time actually does slow down at high speeds. Testerguy had a great example of atomic clocks orbiting Earth. Another good example I know of is how the life span of muons is affected by their velocity:

"Although their lifetime without relativistic effects would allow a half-survival distance of only about 0.66 km (660 meters) at most (as seen from Earth) the time dilation effect of special relativity (from the viewpoint of the Earth) allows cosmic ray secondary muons to survive the flight to the Earth's surface, since in the Earth frame, the muons have a longer half life due to their velocity. From the viewpoint (inertial frame) of the muon, on the other hand, it is the length contraction effect of special relativity which allows this penetration, since in the muon frame, its lifetime is unaffected, but the length contraction causes distances through the atmosphere and Earth to be far shorter than these distances in the Earth rest-frame. Both effects are equally valid ways of explaining the fast muon's unusual survival over distances."

A good example of this is that certain particles with very short lifespans have been observed in real experiments to have extended life when travelling at high speeds - exactly in line with equations. For an external, inertial viewer, the time for the particle has slowed down because it survives longer. For the particle or entity experiencing the velocity, time doesn't even appear to slow down - they experience time at the same rate.

quote: We don't really know this (light not requiring a medium) for certain.

quote: In any event, my observation here is that one cannot affect the speed of a sound wave.

Well, some theorize that light an electromagnetic radiation in general are particles as well as waves, which wouldn't require a medium. Others theorize that the electromagnetic field, for example, is the medium - that all 'fields' are in fact hidden mediums. The difference between light and sound is that we have never found any way to alter the speed of light. You can trivially change the speed of sound, by pressure, temperature, or by medium. Also, different observers can indeed experience sound at a different speed. Consider a moving train, 340m long, at one end of which sits a guy who honks a horn. Relative to the train, the sound will transfer to a second guy at the other end of the train in 1 second. If someone is sat at a station as the train rolls through and observes the same sound being transmitted, and measures the speed of that sound relative to them, they will discover that the speed is the speed of sound PLUS the speed of the train. This is true for all mechanical systems, such as throwing a ball.

However, if we replace the guy on the train with a light and a light switch - both the person on the platform AND the person at the opposite end of the train will measure the speed of light to be exactly the same, regardless of how fast the train is moving. In certain cases this means that certain observers can disagree about the simultaneity of events involving light, which doesn't apply with sound.

quote: However, if you listen to the Doppler Effect, by listening to an ambulance for instance, you'll notice that there are more oscillations as it approaches over a period of, say, ten seconds, than when it leaves. Thus, time is compressed, albeit, to the ear. I am saying that light does the same thing to the eye.

It's important to distinguish the frequency of a wave with its speed. The Doppler effect as it applies to light waves causes similar effects at low speed but vastly different results to sound at higher speeds, because there is a different underlying mechanism. We constantly observe different frequencies of light, or any frequency on the electromagnetic spectrum - but we don't use the frequency of a wave, ever, to calculate time. If light appears at a higher frequency to our eyes, we interpret it as a different colour (in this case a 'blue shift') - we don't interpret that as time speeding up.

quote: The experiment done with the rocket could easily be explained by the effect that gravity has on photons.

I agree that no experiment can ever be devoid of other factors which could potentially be cited, but a wide variety of experiments have been performed which depend on the constancy of light and the time dilation phenomenon.

quote: There is also the fact that, relatively speaking, it doesn't matter which object is expending energy to achieve a difference in velocity. Relatively speaking, if you sit on either the rocket or in the chair, it's not going to make a difference.

This is not correct. See, for you to correctly observe that a clock elsewhere is moving slower than yourself, you yourself have to be in what's called an 'inertial frame'. That is to say, if you held out a mass in front of you, and let it go - it would remain there indefinitely. While velocity is relative and can be undetectable to the observer, acceleration is not (although some scientists have applied thought experiments with gravity to dispute elements of this, that is probably beyond our current discussion). The observer who experiences the acceleration or deceleration to align them with the frame of the original observer does not have this inertial state and thus they are the ones for whom time has slowed down.

If it were true that it made no difference whether you were in the rocket or the chair, both observers would observe that the others clock was running slower than theirs, a logical impossibility. If a < b, b < a is not true.

quote: if we had a different medium in which to observe both train and ball, than light, we would see the ball exceed the speed of light.

Why can we not measure it accurately from an inertial frame, or to put it plainly, simply by being in a particular point in space with no acceleration or forces acting upon us? If we actually did measure the speed of the ball in that scenario, despite the fact that the train is moving 2mph less than the speed of light, and that in the reference frame of the train, the ball is thrown at 4mph in the same direction of the trains velocity, we would observe the speed of the ball to be significantly slower (lorentz contraction, time dilation) such that no matter how fast the ball was thrown, it would never appear to us to be travelling faster than the speed of light. Similarly, if someone shone a light in the same direction of the speed of the train, we would measure the speed of that light as the speed of light. It's almost as though (as Hawking theorized) the speed of light is universal speed limit. The closer you get to it, the more time slows down making any further velocity actually take place over a slower time and thus be reduced. Thus we could never observe the ball to be travelling faster than the speed of light.

Numerous tests of time dilation due to velocity and time dilation due to gravitational distortion have been conducted by using two separate synchronized atomic clocks, placing them in different time dilation frames, and then measuring the difference in their readings taken from the same frame. All of those tests directly dispute your claim that it only appears to.

[quote]since light doesn't require a medium[/quote]Are we really sure about this.. this feels wrong ;)Maybe it is a medium everywhere made of the higgs bossoms or whatever is the smallest bits and pieces :)

Why should it require a medium? If I shot you from a cannon at 500 mph in a vacuum, you will keep travelling at 500 mph until gravity or friction with the intersteller medium slowed you down. A medium is not required for your velocity to be preserved. Sound, on the hand, does not exist in space since it does need a medium - sound is merely waves of compression (the medium can be any matter capable of interacting with all neighbouring particles or molecules).

Light can be impeded by a medium (e.g. being absorbed, slowed down or curved by gravity) but the medium, like your freshly vacuum preserved body, is not necessary to its transmission across distance.